Finite Element Approximation of Time–Fractional Fourth–Order Problem with Nonlocal Diffusion: Existence–Uniqueness and Error Bounds
Abstract
In this paper, we consider a time-fractional fourth-order nonlocal problem with Navier boundary conditions. First, we discuss the existence–uniqueness of the weak solution at the continuous level using Faedo–Galerkin method. Then this fourth-order problem is transformed into a system of two second-order equations. For this system, a fully discrete scheme is proposed which comprises the standard finite element method and the [Formula: see text] scheme on the graded mesh. For the proposed scheme, we derive [Formula: see text]-robust convergence estimates. Finally, numerical experiments are presented to validate the theoretical findings.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Advanced Numerical Methods in Computational Mathematics
Differential Equations and Boundary Problems
Publication details
- Journal / source
- International Journal of Computational Methods
- Volume
- 23
- Issue
- 07
- Publication date
- 29 January 2026
- Language
- EN